| The static and dynamic nonlinear behaviors of three-dimensional long-span cable-stayed bridges under gravitational and seismic loading are studied. The cases of multiple-support and uniform seismic excitations are considered; furthermore, effects of non-dispersive travelling seismic waves on the bridge response are studied. Different sources of nonlinearity are included in the analysis using the large deflection theory. Nonlinearities are due to: (1) changes in cable geometry with tension changes (the sag effect), (2) axial force-bending moment interaction in the bridge girder and towers, and (3) change of geometry of the whole bridge due to large displacements. A tangent stiffness iterative procedure is utilized in the analysis to capture the nonlinear seismic response. Numerical examples are presented in which a comparison is made between a linear earthquake-response analysis (using the tangent stiffness matrix of the bridge in the dead-load deformed state), and a nonlinear earthquake-response analysis using the step-by-step integration procedure. In these examples, two models having center spans of 1100 ft and 2200 ft are studied; this range covers both present and future designs. Based on this investigation, the following conclusions can be made: (1) Multiple-support seismic excitations can have a significant effect and should be considered in the analysis, (2) The travelling seismic wave effect, in terms of time delay and phase difference, should also be considered, (3) Geometric nonlinearity should not be ignored when computing the earthquake-response of these long contemporary bridges, especially when considering the future trend of increasing the span length, (4) Although for the present range of center spans (up to 1500 ft), linear dynamic analysis is adequate, nonlinear dead-load analysis is still essential to start the linear dynamic analysis from the dead-load deformed state, (5) There is strong coupling in the three orthogonal directions within each mode of vibration, moreover, several modes will in general contribute to the total dynamic response, (6) The P-{dollar}{bsol}Delta{dollar} effect in the bridge deck and tower legs should be considered in the analysis, and finally, (7) Energy-absorption devices and special bearings should be provided at the supporting points to reduce the seismic response of the bridge. |
